Static critical behavior in the inactive phase of the pair contact process

Steady state properties in the absorbing phase of the $1d$ pair contact process (PCP) model are investigated. It is shown that, in typical absorbing states (reached by the system’s dynamic rules), the density of isolated particles, ${\rho }_1$, approaches a stationary value which depends on the annihilation probability ($p$); the deviation from its ‘natural’ value at criticality, ${\rho }_1^{nat}$, follows a power law: $\rho_1^{nat}-\rho_1 \sim (p-p_c)^{\beta_1}$for$p>p_c$\mathrm{.}MonteCarlosimulationsyield$\beta_1=0.81$. A cluster approximation is developed for this model, qualitatively confirming the numerical results and predicting ${\beta }_1=1$. The singular behavior of the isolated particles density in the inactive phase is explained using a phenomenological approach.